Problem: Simplify the following expression: $ a = \dfrac{-8}{3} + \dfrac{-6n + 7}{n + 6} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{n + 6}{n + 6}$ $ \dfrac{-8}{3} \times \dfrac{n + 6}{n + 6} = \dfrac{-8n - 48}{3n + 18} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-6n + 7}{n + 6} \times \dfrac{3}{3} = \dfrac{-18n + 21}{3n + 18} $ Therefore $ a = \dfrac{-8n - 48}{3n + 18} + \dfrac{-18n + 21}{3n + 18} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-8n - 48 - 18n + 21}{3n + 18} $ $a = \dfrac{-26n - 27}{3n + 18}$